How many students can a van carry? How many students can a bus carry?

Question

The senior classes at High School A and High School B planned separate trips to the water park. The senior class at High School A rented and filled 12 vans and 14 buses with 556 students. High School B rented and filled 1 van and 14 buses with 457 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry? 

We need to find out what x and y represents and the system of equations.

Answer 1

x = # of students per bus

y = # of students per van

14 x+ 12y = 556

14x + y = 457

subtracting the equations, x cancels out

11y = 99

y=9

van holds 9 students

bus holds x = (457 - 9)/14 = 32

Answer 2

Patrick, The Tutor above, did an excellent job of showing the systems of equations. You have to define X and Y. One thing to note that always helped my students, is to see that there are two separate buses or two separate things presented in systems of equation problems. Noticed that bus A is a sentence so stop at the end of the sentence to write your first equation. Then proceed forward to the next sentence pertaining to Bus B and write an equation given all the information. Everything is given for X and Y and each sentence.